Sum to Infinity Calculator
🔁 Sequences & series. Use the Sum to infinity (geometric) formula to find sum to infinity, first term a, common ratio r: pick the value you want, type the others, and the answer updates as you go.
Pick the ○ next to the value you want to find, fill in the others, and it solves as you type.
What each letter means
| Quantity | Unit |
|---|---|
| Sum to infinity | no unit |
| First term a | no unit |
| Common ratio r | no unit |
Worked example
Find the sum to infinity when First term a = 4, Common ratio r = 0.5.
Using S_∞ = a/(1 - r), |r| < 1: Sum to infinity = 8.
Frequently asked questions
What is the formula for Sum to infinity (geometric)?
S_∞ = a/(1 - r), |r| < 1.
What do the letters stand for, and what units are used?
Sum to infinity, First term a, Common ratio r.
How do you calculate sum to infinity?
Put the values into S_∞ = a/(1 - r), |r| < 1. For example, with First term a = 4, Common ratio r = 0.5, sum to infinity = 8.
Can I solve for a different value?
Yes. In the calculator above, pick the circle next to any value (sum to infinity, first term a, common ratio r) and fill in the others: it rearranges the formula for you.
